Overround Decomposition in European Football Markets: An Empirical Analysis of 2,490 Closing Lines
Quantitative derivation of bookmaker margins, proportional and Shin models, and predictive scores on 2,490 Premier League matches (2019–2026, source football-data.co.uk).
Abstract
This empirical study analyses 2,490 closing lines from the English Premier League across seven consecutive seasons (2019–20 to 2025–26, source football-data.co.uk) to quantify how bookmakers price match outcomes. Overround on closing lines averaged 2.70% at Pinnacle and 4.16% for the market average. Evaluating four margin-stripping engines (Multiplicative, Additive, Power, and Shin) on Pinnacle closing lines yielded similar rounded aggregate predictive scores: Brier scores stood at 0.5676 across all four models (differences < 0.0001), with log-loss between 0.9583 and 0.9584. On the 1X2 EPL market, Shin adjustments shift probability weight relative to multiplicative normalization by +0.79 percentage points on favorites (<1.70, 953 selections), +0.10 pp on mid-range odds (1.70–3.50, 2,848 selections), and −0.28 pp on longshots (>3.50, 3,669 selections). Flat staking returns on Pinnacle closing odds range from −0.32% to −5.51%. We release the raw dataset and Python replication script for open scientific verification. Each reported 95% interval compares one odds band with zero. Those intervals do not test differences between bands or a trend. A predeclared contrast or trend with match-level clustering is needed; that comparison is not reported here.
1. Introduction & Theoretical Framework
In financial economics and sports wagering markets, closing odds represent the consensus probability distribution conditional on all publicly available information. However, bookmakers embed an overround (vigorish) such that the sum of implied probabilities strictly exceeds unity. Proportional normalization divides each inverse odd by the market overround, assuming uniform margin loading. Conversely, Hyun Song Shin (1991, 1993) formulated an equilibrium model wherein informed traders induce an asymmetric margin distribution to protect the bookmaker against adverse selection.
The primary challenge for quantitative analysts is extracting true implied probabilities P*(E) from observed odds. Using 2,490 Premier League matches from 9 August 2019 to 8 January 2026 (source football-data.co.uk), we investigate margin distributions across Pinnacle and broader market closing prices.
2. The 2,490 Closing Lines Dataset
Our empirical investigation compiles 2,490 closing lines for 1X2 (Home / Draw / Away) markets spanning English Premier League fixtures from 9 August 2019 to 8 January 2026, obtained from football-data.co.uk. The dataset contains opening and closing decimal odds for Pinnacle and market averages. Closing overround averaged 2.70% for Pinnacle and 4.16% for market averages across the seven covered seasons.
3. Mathematical Models of Margin Extraction
We implement and compare four formal margin-stripping engines across all 2,490 matches: Multiplicative (proportional normalization), Additive, Power, and Shin's information-theoretic model.
Assumes bookmaker margin is distributed strictly proportional to implied probabilities across Home, Draw, and Away outcomes.
Where z represents the proportion of insider bettors, calibrated via nonlinear root finding such that Σ P*(E_i) = 1.
4. Empirical Findings & Distribution Analysis
Across the 2,490 matches, Pinnacle closing overround averaged 2.70% (2019–20: 2.86%, 2020–21: 2.39%, 2021–22: 2.45%, 2022–23: 2.46%, 2023–24: 2.93%, 2024–25: 2.99%, 2025–26: 2.95%), while market average overround averaged 4.16% (reaching 5.45% in 2025–26). De-vig evaluation on Pinnacle closing lines yielded Brier scores of 0.5676 across multiplicative, additive, power, and Shin methods (difference < 0.0001) and log-loss between 0.9583 and 0.9584. Similar rounded aggregate Brier and log-loss scores do not establish calibration or predictive equivalence. Calibration needs reliability assessment; equivalence needs a specified tolerance and paired uncertainty analysis.
Table 1: Overround Distribution by Premier League Season (N = 2,490)
| Season | Fixtures | Pinnacle Close (%) | Market Avg (%) |
|---|---|---|---|
| 2019–20 | 380 | 2.86% | 4.07% |
| 2020–21 | 380 | 2.39% | 4.21% |
| 2021–22 | 380 | 2.45% | 3.87% |
| 2022–23 | 380 | 2.46% | 3.90% |
| 2023–24 | 380 | 2.93% | 3.97% |
| 2024–25 | 380 | 2.99% | 4.19% |
| 2025–26 | 210 | 2.95% | 5.45% |
| OVERALL (2019–2026) | 2,490 | 2.70% | 4.16% |
Table 2: Probability Adjustment: Shin vs. Multiplicative Model by Odds Tier (N = 2,490)
| Odds Tier | Sample Count | Delta (Shin - Mult) |
|---|---|---|
| Heavy Favorites (< 1.70) | 953 | +0.79 pp |
| Mid-Tier Markets (1.70 – 3.50) | 2,848 | +0.10 pp |
| Longshots / Unders (> 3.50) | 3,669 | -0.28 pp |
5. Practical Implications for +EV Staking
Shin's method adjusts fair probabilities relative to multiplicative normalization: favorites (< 1.70, 953 selections) receive +0.79 percentage points on average, mid-tier prices (1.70–3.50, 2,848 selections) receive +0.10 pp, and longshots (> 3.50, 3,669 selections) shift by −0.28 pp. Flat staking 1 unit on Pinnacle closing odds yields returns from −0.32% (odds 1.50–2.00, 95% CI: −6.00% to +5.36%) to −5.51% (odds > 10.00, 95% CI: −47.55% to +36.54%). On market average closing odds, losses on longshots above 5.00 are higher (−6% to −10%). Each reported 95% interval compares one odds band with zero. Those intervals do not test differences between bands or a trend. A predeclared contrast or trend with match-level clustering is needed; that comparison is not reported here.
6. Conclusion & Open Data Availability
This paper establishes empirical benchmarks for Premier League 1X2 overround distributions based on 2,490 matches from football-data.co.uk. The complete dataset (/papers/epl-closing-lines-2019-2026.csv), documentation (/papers/README-epl-closing-lines.md), and Python analysis script (/papers/epl_closing_lines_analysis.py) are licensed under Open Data Commons Attribution (ODC-By v1.0) and freely accessible.
Academic References
- Shin, H. S. (1991). Optimal betting odds against insider traders. The Economic Journal, 101(408), 1179-1185.
- Shin, H. S. (1993). Measuring the incidence of insider trading in a market for state-contingent claims. The Economic Journal, 103(420), 1141-1153.
- Clarke, S. R., & Norman, J. M. (1995). Home ground advantage of individual clubs in English soccer. Journal of the Royal Statistical Society: Series D (The Statistician), 44(4), 509-521.
- Dixon, M. J., & Coles, S. G. (1997). Modelling association football scores and inefficiencies in the football betting market. Journal of the Royal Statistical Society: Series C (Applied Statistics), 46(2), 265-280.
- Kelly, J. L. (1956). A new interpretation of information rate. Bell System Technical Journal, 35(4), 917-926.
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